The structure of the simulated annealing algorithm is presented and its rationale is discussed. A unifying heuristic is then introduced which serves as a guide in the design of all of the sub-components of the algorithm. Simply put this heuristic principle states that at every cycle in the algorithm the occupation density should be kept as close as possible to the equilibrium distribution. This heuristic has been used as a guide to develop novel step generation and temperature control methods intended to improve the efficiency of the simulated annealing algorithm. The resulting algorithm has been used in attempts to locate good solutions for one of the lens design problems associated with this conference viz. the " monochromatic quartet" and a sample of the results is presented. 1 Global optimization in the context oflens design Whatever the context optimization algorithms relate to problems that take the following form: Given some configuration space with coordinates r (x1 . . x) and a merit function written asffr) find the point r whereftr) takes it lowest value. That is find the global minimum. In many cases there is also a set of auxiliary constraints that must be met so the problem statement becomes: Find the global minimum of the merit function within the region defined by E. (r) 0 j 1 2 . . . p and 0 j 1 2 . . . q.

By examining aspherical surface aberration contributions it is shown that aspheres can be used to simplify zoom lens construction and to improve image quality by allowing the designer to selectively correct aberrations at different zoom positions. 1.

Global Optimization (GO) is an area of applied mathemetics that has been active for many years. A large variety of GO algorithms have been constructed in an effort to find a solution to the general GO problem. Some of these have proved to be successful on certain classes of problems. However no general deterministic algorithm exists that can locate the global optimum for every multidimensional problem. Traditionally in the lens design discipline the search for an optimum solution in the design space has been done by optimization methods. The conventional design methods are in principle local search methods and do not pmvide any global information on the design space. As the available computer power increases GO tools can be used also in optical design. A two phase search algorithm based on global optimization techniques is described. In a first phase using a coarse sampling approach the program finds the favorable regions that correspond to potentially promising configurations. In a second phase conventional optimization routines are used to find the best solutions in eh region. Then an optimum solution is determined according to the application at hand. The pro algorithm is analyzed and compared to more conventional design approaches. A further refmement of the algorithm excludes from the systematic search some unfavorable configuration regions through the use of a simple expert system. Search times are further reduced through parallel-processing methods. We believe this approach to lens design represents new initiative towards the determination of the optimum solution in any lens design problem. 1.

The new decade will bring a wide variety of new developments in optical design. Some of these will be in response to new technologies such as binary optics or the use of optical liquids for secondary color correction. Others will include I hope a new appreciation for how the intelligent use of classical ideas can lead to large improvements in the performance of designs.

Forward looking infrared optics defocus with temperature change due to the materials employed. Methods of elimination this defocus - mechanical, electro-mechanical and optical - are discussed and evaluated.

A new automatic lens design method using singular value decomposition (SVD) is proposed. This method enables the designer to reflect his own intention in optimization via the Rank Down Constant introduced in this paper. This characteristic also makes it possible to accelerate the optimization. An example showing the high performance of this method is demonsirated. Some useful applications of S. V. D. are also proposed. 1 .

Spherical aberration in a flat surfaced radial gradient-index lens (a Wood lens) with a parabolic index profile can be corrected by altering the profile to Include higher order terms. However this results in a large amowfl of third order coma. This paper presents an alternative method of aberration correction similar to that used in the catadiopthc Schmidtsystem. A Wood lens with a parabolic profile is used to provide all or most of the optical power. Coma is corrected by stop shifting and Spherical aberration is corrected by placing a powerless Wood lens corrector plate at the stop. 1.

A review of the methods employed to compute the wavefront
shape, the point spread function and the optical transfer function in
lens evaluation programs is presented. One of the simplest methods to
perform numerical calculations of the diffraction performance of
optical systems is to divide the aperture in small squares, as
suggested by H. H. Hopkins (1957), and then to consider the wavefront
in each of these small squares to be flat and perpendicular to the ray
direction in that region. This method however, presents some
limitations, since the wavefront has to be flat within a fraction of
the wavelength in that small square. This might not be the case if the
wavefront is either too aberrated, or the defocusing is too large.

Simultaneous alignment and figure testing have been simulated by computer for components of a Cooke triplet and a two-. Petzval telescope using end-to-end wavefront aberration measurement and computer model reverse optimization. Experimental confirmation is discussed. 2.

Purely diffractive doublets are corrected on-axis at two wavelengths. The doublets are then optimized with respect to their design parameters to achieve wideband imaging on-axis. Completed extensions to this design are also described. 2.

The sensitivity of infrared optical designs to errors in dispersion is explored through the use of examples. The main cause for a high sensitivity to dispersion tolerances in achromatic designs is explained. Conditions for alerting the optical designer to the need for including dispersion tolerances in the design process as well as to suspect raw refractive-index data for an infrared material are provided. 2. OVERVIEW OF CONCEPTS Dispersion tolerances (dV) rarely limit the performance of optical systems used in the visible spectral band. An optical designer might consider dispersion tolerances on the glasses in a visible-band design when the design has a very high-performance specification and/or when there is very little performance margin for tolerances. In infrared (IR) designs dispersion tolerances are even more rarely considered for the materials. It is also unusual to tolerance the bulk refractive index change (index tolerance dn) for an IR design. The need for dispersion tolerances are analyzed in this paper to highlight for the optical designer the situations and motivations for including dispersion tolerances in the evaluations of optical designs especially in the infrared. Achromatic optical systems in the infrared show a wide range of sensitivity to changes in dispersion. The sensitivity is driven by V-number difference (LV) of the materials used to achieve achromatization and to some extent by aperture diameter and f-number. Therefore the sensitivity to change in dispersion of the materials

The SYNOPSYS - expert-systems program XSYS - is a radical departure from traditional methods of lens design. I describe typical problems that were presented to XSYS and show how the program can find useful sometimes unexpected starting points. 1.

A timesaving simplified calculation method by means of the 3rdorder spherical aberration coefficient has been developed to evaluate the root mean square (RMS) wavefront error change of a moisture absorbed aspherical plastic singlet for an optical disk. 1.

Design procedures for simple two- and three-element diffractive telescopes are described. The basic configuration for the two-element design is obtained analytically by solving design equations to set the Seidel aberrations to target values. Computer optimization is used to complete the design of the doublet and triplet telescopes. It is shown that diffraction limited performance can be obtained from these diffractive systems. 1.

A new, coordinate-free version of the exact ray-trace equations for optical systems consisting of conic reflecting, refracting and reference surfaces is presented. These equations are differentiated to obtain closed-form optical sensitivity dyadics. For computation, the sensitivities are evaluated in a single global coordinate frame and combined in linearized ray-trace matrix difference equations that propagate the rays and the sensitivities from element to element. One purpose of this analysis is to create optical models that can be directly integrated with models of the instrument structure and control systems for dynamic simulation.

Hybrid refractive-diffractive elements have the potential to provide chromatic correction with less than half the material content of a conventional doublet. It is shown that the performance of a general hybrid meniscus element can exceed that of the equivalent doublet. Their design and potential advantages are illustrated to good effect in a Petzval objective example. 1.

A novel configuration for a wide angle flat field all reflective unobscured telescope using two figured surfaces which are easily fabricated and aligned is described. DESCRIPTION OF TELESCOPE This paper describes an easily fabricated telescope which forms a high quality image of an extremely wide angle object field on a flat image surface. The telescope uses only reflectors and thus has no chromatic aberrations. An eccentric portion of the rotationally symmetrical field of the telescope is used such that no part of the aperture is obscured. The mirrors are surfsces of revolution described exclusively as flats spheres or conic sections all of which are easily tested and verified in manufacwre using well-known conventional null tests. Each mirror shares a common axis of rotational symmetry facilitating telescope alignment. One mirror is used twice providing the function of a secondary and tertiary mirror while eliminating the need to fabricate and align a separate tertiary mirror. The current design evolved from a form pcpularly known as the WALRUS'' a three mirr rotationally symmetric flat field unobscured design arranged in a " Z" configuration with an aperture stop between the secondary and tertiary mirrors (figure 1). In the WALRUS patent the two concave mirrors are specified as an effipsoid (secondary mirror) and a sphere (tertiary mirror) while the convex (primary) mirror is a sphere. The base curvatures of the three powered mirrors are chosen such

Optical components such as lenses beamsplitters etc. can be fabricated and integrated on single substrates by using photolithographic techniques. This allows to build integrated free-space optical systems for a variety of applications without the need for costly mechanical alignment. I.

The wavefront variance merit function is constructed with aberration orders identified and partitioned. The partitioned merit function topographies of three optical systems are examined. 1. INTRODUCFION The study of the behavior of individual wavefront aberration coefficients with respect to optical system parameters has long been successfully employed to gain insight into the properties of optical systems. However for many optical systems it is more appropriate to examine the wavefront aberrations collectively rather than individually. New insight into the imaging characteristics of optical systems may be obtained by using the individual wavefront aberration coefficients to construct the average wavefront variance function. This can be done in such a way that the merit function may be separated into partitions which are associated with a single aberration order. The partitions are a small number of image quality indicators that may be examined individually. Each indicator ifiustrates the behavior of the optical system at a particular aberration order. 2. FORMULATION OF THE MERIT FUNCTION The wavefront variance merit function is defined by K w2 )ftuld '' (1) where the angle brackets denote averaging over the pupil or field as indicated in the equation and W is the wavefront aberration function as a function of pupil position p. and field position H. For axially symmetric optical systems the aberration coefficients are introduced by writing the wavefront aberration function as a Taylor series expansion in p and

Designers are often asked to optimize the modulation transfer function (MiT) of a particular lens at specific fields and spatial frequencies. Use of a merit function related to mean square spot size or wave aberration to achieve these goals frequently requires considerable designer intervention. We describe an algorithm whereby diffraction MTF is optimized directly. The algorithm is efficient enough (i. e. on the order of five times the run time for classical techniques) to be used as a practical design tool. To illustrate use of the algorithm a previously designed night vision objective lens is reoptimized with the goal of increasing the MTF at a particular spatial frequency thus increasing the modulation margin allowed for tolerancing. Significant improvements in MTF and depth of focus are achieved with minimal designer effort and reasonable computation times. 1 .

An exact raytrace (Snell''s law refraction) of the discontinuous surfaces of kinoforms (surface relief lenses) can explain their optical performance at different wavelengths without diffraction. A phase-based merit function generated by raytracing can be used to design and optimize systems containing both kinoform and conventional optical surfaces.

The practical use of Generalized Simulated Annealing (GSA) optimization is explored to determine additional benefits beyond the global minima location capability. In particular a means of using the strengths of both GSA and Damped Least Squares (DLS) optimization techniques is examined in order to increase the amount of usable information and to enhance usefulness in a microcomputer environment. 1. BACKGROUND The optimization ofthe performanceofan opticalsystem is most often performed bydamped leastsquares (DLS) techniques. This methodand its variants has proven to beeffective for the reduction ofsystem merit functions overa broad range ofproblem types with quite rapid convergence rates. The effectiveness of DLS optimization will often depend on the quality of the starting point the construction of the merit function and the proximity of the starting point to local minima ofthe merit function. The characteristic of the DLS technique to compute an optimum solution to minimize the merit function based on the instantaneous first and in some cases second partial derivatives gives rise to the technique''s strongest and weakest points. The strongest point is its rapid convergence while the weakest point is the inability to escape local minima in order to locate a superior local minima or the global minima. The strength of rapid convergencewas important when the majority oflens design programs where on a mainframe computers were processing time is costly. The inability to escape local minima weakness was most often overcome

The design for a telescope is presented which calls for small optical components in an all-reflective wide-field-of-view phased-array configuration. Attention is given to the geometric phasing conditions and other phasing requirements for the phased-array design, and analytical expressions are set forth for the paraxial relations and distortion. The design of the subtelescopes is based on a three-mirror design, and particular attention is given to the problem of subtelescope field curvature. It is shown that several configurations provide the required corrections for the field curvature and the stigmatic aberrations. Subtelescope aberrations such as coma can affect optical phasing, which indicates that a tolerance analysis conducted aberration-by-aberration is necessary for developing the all-reflective configuration.

Considering the real pupil curvatures the new exact sine condition in the presence of spherical aberration is derived and its validity is confirmed by ray traces. This new exact sine condition is useful for lens designing and lens evaluation. 1.

A telescope is described that can be used for high-power-laser optical communication links between satellites. An all-refractive design is selected because it is preferred for the application, and the performance specifications are listed for the novel technologies associated with implementation. The telescope is intended to measure 150 x 150 x 350 mm and have a 100/8-mm outside/inside diam ratio and a total FOV ratio of 1.0/12.5 deg exterior/interior. Detailed descriptions are given for telescope components including the collimator, eye piece, scanners, and the pupil imager, and the resulting values for wave-aberration RMS and distortion are discussed. The resulting telescope is found to be about twice as good as the specifications require allowing suitable tolerances for the manufacturing of the telescope.

Some effective usage of the radial GRIN lens in camera zoom systems are presented and
lens design examples are shown. Also, effective Abbe number of a cemented GRIN lens is
discussed and it is shown that a GRIN lens with uncomon dispersion can be replaced by the
cemented GRIN lens with common disparsion.

This telescope is exactly one power and has an objective, an
erecting relay and an eyepiece. As can be seen in the
diagram the direction of any object seen at the Entrance
Pupil has the exact same direction at the Exit Pupil over the
whole of the field of view assuming that the system.is
completely corrected for distortion. If this is in fact the
case then the direction of any object as seen at the Exit
Pupil is constant as the axis of the telescope is rotated.
This is the pure definition of a CONSTANT DEVIATION DEVICE.

e describe the various principles used in our optirnizatic'i programs which were developped in a more consequent manner ttlaIl it as done for other known proqramns. The iterative optirnization process in lens design consists ot tio main parts: The use
01: the so called Linear Model and the dynamic adaption to the
actual conditions. Corresponding to that the discussion in this
paper is built up.

Ray-tracing through Progressive Addition Lenses (PAL) has been performed. PAL is a deep non rotationally symmetric asp1ric lens used for the compensation of presbyopia. PAL and its mathematical model are presented. The special features of the ray-tracing program due to the model of the lens plus eye system are detailed. Typical results are presented showing in particular that computing conditions of contour-plots of power and astigmatism must be very strict and that coma must be taken into account for precise measurements of PAL. 1.

This article addresses the impact of nonlinearity on the problem of designing lenses and the connection of Newton''s method with ordinary differential equations (ODE''s) and describes a method for improving its convergence inspired by the total least squares problem. A possible subtitle for this article might be " Why Haven''t All Possible Lenses Been Designed Already?" I first heard that question asked by Dr. Kingslake when he visited Itek over 15 years ago when we were demonstrating our computer lens design capabilities to him. It''s a question that comes to mind when one contemplates that there are more designers around today than back in precomputer times each of today''s designers can do more computation in a couple of days than a precomputer designer could do in a lifetime and very many different lens forms were already discovered by the time the computer came into use. So one might begin to wonder how many lenses are there? Or more in he spirit of this article how many solutions are there to the nonlinear equation of the lens design problem? In response to this question consider Fig. 1. This is a montage of sixelement lens forms gleaned from several books on the history of the photographic objective about which Dr. Kingslake has written extensively1. The lens forms shown are all from precomputer times and it is evident that there were a large number

As we know, wave aberration is the difference between the ideal wave and the
real wave. One of the important characteristics of ordinary optical system images is
the condition of equal optical path distance. If all light from a point A passing
through the optical system focuses at A', we can say that point A' is the ideal
image of object point A and that the optical path distances of all rays from A to A'
are the same. When there is aberration in the optical system, wave aberration is the
difference of geometric path distances multiplied by the index. In figure 1 wave
front P from point B passing through the optical system forms a new wave surface
pp'. Generally we use the intersection point ' of the principal ray and the ideal
imaginary surface as the center of the ideal reference spherical surface P"P" so P"P
is the wave aberration

Often it is not possible to fix pairs of infrared refractive materials in the
γv-v diagram to design achromatic doublets with focal distance thermal change, matching the expansion of the focal plane supporting structure. The problem can be
solved with three refractive materials if they form a finite area triangle in the
γV-V diagram. We derive formulas for the calculation of the power of the
elements that include both the doublet and the triplet solutions.

T types of zoan lens with aspherical surfaces for camcorder has been
succssfu11y design1 . The first type has single aspherical glass lens , axx
realizes sizeruction of 30% than cxxiventicxal zocxn lens. Ar the secori type
consists of light-weight plastic lenses with aspherical surface in order to ru weight of zoan lens.

Neural Networks are part of a revived technology which has received a lot of hype in recent years. As is
apt to happen in any hyped technology, jargon and predictions make its assimilation and application difficult.
Nevertheless, Neural Networks have found use in a number of areas, working on non-trivial and non-contrived
problems. For example, one net has been trained to "read", translating English text into phoneme sequences. Other
applications of Neural Networks include data base manipulation and the solving of routing and classification types
of optimization problems.
It was their use in optimization that got me involved with Neural Networks. As it turned out, "optimization"
used in this context was somewhat misleading, because while some network configurations could indeed solve certain
kinds of optimization problems, the configuring or "training" of a Neural Network itself is an optimization problem,
and most of the literature which talked about Neural Nets and optimization in the same breath did not speak to my
goal of using Neural Nets to help solve lens optimization problems. I did eventually apply Neural Network to lens
optimization, and I will touch on those results. The application of Neural Nets to the problem of lens selection was
much more successful, and those results will dominate this paper.

A static computer-aided method used to align a visible wavelength grazing incidence ring resonator for a free-electron laser (FEL) is presented with a brief description of the hardware, results of numerical simulations, and actual initial data. A computer-aided alignment scheme is particularly useful for this application due to the optical system complexity and the need for precise results. Although the system hardware has not yet been perfected, initial data shows that this technique works and presents a viable solution to this alignment problem. Utilizing information from an interferogram taken at a single axial field point and information about the chief ray of the optical system, it is shown that it is possible to converge to an alignment solution using a constrained damped least squares optimization in a commercially available lens design package.

In this paper we propose a nonlinear model which can be considered as a mathematical programming problem with linear and quadratic constraints to design the optimal tolerance of a lens system. Owing to the negligence of the nonlinear property of a optimized lens system the existing studies on the tolerance design are unable to solve the optimal tolerance design problem. For realizing this purpose i. e. maximizing the tolerance of the lens system we propose a nonlinear model which can be considered as a mathematical programming problem with linear and quadratic constraints to design the optimal tolerance of a lens system. Assuming X (x1 . . . x 2'' EJ and ''F(X) are parameters of a lens system manufacturing error for each parameter and merit function of the image quality respectively. The following statements are supposed adequately. (A1) The probability density of k N(o that is Ek is normal distribution with zero mean and variance a. (A2) The difference of the merit function between the real system and the design system can be approximately expressed by quadratic expression. 4(X+cr)(X) c3a: E1 (1) where V () and H () (A3) The purpose of the optimal tolerance design is to determine the variances (a . . . a) of (E1 . . . E and satisfy the following conditions: (i) D(M) (ii) M(L4) m (2) (iii) E po as great as possible

The use of electronic computers in optical design and analysis is well
established. In fact, optical calculations were among the first
applications of the first computers that were built in the 40's, and
Donald Feder, starting in 1951 [1], proved that the use of these
machines went far beyond removing the tediousness of laborious
calculations and offered new dimensions in understanding the actual
design process [2]. By today's standards, of course, the equipment
which had such a remarkable impact at its time, was primitive and
slow. A modern inexpensive programmable calculator easily outperforms
the any computers in both speed and memory capacity, not to mention
accuracy and reliability. This also implies, that today, even
computers at the low end of the cost and performance scale can be
turned into remarkably powerful tools for optical design and analysis.
This has been demonstrated for the class of programmable calculators
[3] but applies, of course, even more convincingly to the present
generation of low-cost personal computers, which are typically based
on 16- or 32-bit processors, and where prices start well below
$ 1000.-. Any degree of higher performance is available at steadily
increased prices, so that there appears to be a fit for each
requirement.

The baseline multiaperture echelle spectrometer for the Atmospheric IR Sounder (AIRS) is described in terms of design and applications. The functional requirements for the optical design are set forth including the 1-K measurement goal, the 3.4-15.4 spectral bandpass, and the full global coverage twice daily. The multiaperture spectrometer is compared to the cross-dispersed spectrometer, and the multiaperture model is found to permit specific adjustments to the signal-to-noise ratio. The optical design of the spectrometer is described in terms of the focal-plane constraints, the multiaperture pupil-imaging relay, the spectrometer collimator, and the grating format and efficiency. The multiaperture design is found to have a good spectral-response function, and a 1.2 percent signal change is noted for a 95-percent unpolarized scene. The AIRS instrument is illustrated in its deployment configuration and is concluded to be capable of fulfilling the performance requirements.

A problem can arise when a set of optics must be aligned but intrinsic surface errors
dominate alignment wavefront errors. Aligning diamond-turned optics interferometrically at
visible wavelengths is one such example. Diamond-turned optics can exhibit a high-spatialfrequency
surface ripple from the machining process, which, in many cases, can render an
interferogram unintelligible to the point that even serious alignment errors cannot be detected.
In an alignment demonstration conducted last year this problem was encountered head on
and two techniques were applied to extract meaningful wavefront data. The first relied on
spatial filtering of the return wavefront to smooth out the effects of high-slope surface errors.
This approach showed potential in that it is a simple method that can be easily applied. The
second approach used a new software algorithm, available as part of the Zygo Mark lV phase
measuring interferometer, where regions of fringe discontinuities are discarded and the
resultant piece-wise phase map is reconstructed as a continuous wavefront. Using this latter
approach, we were able to precisely align a three-mirror telescope comprised of diamondturned
mirrors and used in a double-pass configuration. The approaches to be described are
applicable to the alignment of infrared and visible sensors and metrology of single surfaces.

Optics for head-up displays (HUDs) with two combiners are reviewed with respect to aberration correction and the optimization of the azimuth field. The impetus for utilizing two combiners is discussed by comparison with conventional HUD designs, and the requirements for aberration correction are listed. The use of a CRT that incorporates the P-53 phosphor is shown to increase the azimuth instantaneous FOV (IFOV), and HUDs with dual combiners enhance the elevation IFOV. A dual-combiner HUD is shown to require a P-1 phosphor CRT, improved color correction, a reduced Petzval sum, and aberration control that is extended over more of the pupil as compared to single-combiner HUDs. The P-53 phosphor can be used to filter spectral sidebands and thereby permit the use of a lens that is not capable of good chromatic correction as well as enhance the azimuth IFOV without changing the module depth.

The design process for an all-reflective zoom telescope is presented. Special consideration is given to the development of the starting configuration and the subsequent optimization process. The non-traditional optimization route utilized as a result of the unusual pupil characteristics of such an all-reflective zoom system is examined. Results of the design are presented.

For the past year or so, we have been exploring a technique for finding potential solutions of
what might be called the generalized imaging problem. The underlying hypothesis is that any basic
imaging problem can be solved, if at all, by using not more than two generic lenses. A generic lens can
comprise a number of elements to affect aberration control, distribute power, etc. Application of this
technique yields a plot of regions where potential solution may exist (conversely, regions where solution
do not exist). Typically, the abscissa and ordinate are the powers of the two lenses. Once a "power
pair" is chosen for evaluation, the spatial positions of the lenses are readily calculated. This technique
will be discussed in detail in an upcoming paper.
After some success was realized in employing the method to fixed geometries, we investigated
its application to finding possible regions of solutions for problems involving zoom lenses. Although the
same technique is employed to find potential solutions, presentation of the information for use by the
designer is significantly more involved than when dealing with the fixed geometry case. Various
parametric constraints can be imposed to appropriately limit solution space. Further discussion of this
subject will be contained in the aforementioned paper.

The proposed procedure works on the basis of a merit function of the 4th degree and is used for the optimization of the Seidel image errors of a system composed of thin lenses by means of lens bendings. Between the thin lenses air spaces may exist. All solutions which lie within the permissible intervals of bending are taken into consideration when the sums and the corresponding surface contributions of the Seidel image errors are situated below a limit that may be selected at will. The search for a relative minimum is successful too if a relative maximum lies on the path to the relative minimum. The procedure is especially suitable when in a given system thin lenses are preferred for reasons of weight material price transmission or broadband colour correction. 1. Procedure Lens bending means equal curvature change at each